Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	59×	body	1280	valid
3.0ms	139×	body	80	valid
2.0ms	24×	body	640	valid
1.0ms	24×	body	320	valid
0.0ms	10×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
42.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify225.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune733.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	602	3	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	603	3	606

Merged error: 0.2b

Counts

606 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

15.0b	(/ x (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.2b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

8.0ms	(/ x (- (* x x) (* 1.0 1.0)))
8.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
8.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
1.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ x (- (* x x) (* 1.0 1.0)))
42.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
37.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
184.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	393	1262
1	1600	1156
2	5001	1097

prune405.0ms

Filtered

141 candidates to 114 candidates (80.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	4	144

Merged error: 0.2b

Counts

144 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

15.0b	(/ x (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.2b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

5.0ms	(/ x (- (* x x) (* 1.0 1.0)))
8.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
8.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
1.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ x (- (* x x) (* 1.0 1.0)))
43.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
37.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
187.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	393	1262
1	1600	1156
2	5001	1097

prune504.0ms

Filtered

141 candidates to 114 candidates (80.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	140	5	145

Merged error: 0.1b

Counts

145 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

15.0b	(/ x (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.2b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

6.0ms	(/ x (- (* x x) (* 1.0 1.0)))
13.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
8.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
1.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ x (- (* x x) (* 1.0 1.0)))
42.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
38.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
185.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	393	1262
1	1600	1156
2	5001	1097

prune574.0ms

Filtered

141 candidates to 114 candidates (80.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	141	5	146

Merged error: 0.1b

Counts

146 → 5

regimes39.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.3b

bsearch101.0ms

Steps

Iters	Range		Point
9	0.09117784756913819	2697524.489058797	9138.442026599892
9	-39258024566.25627	-1421.6155834850151	-12739.391686969833

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	34
1	57	34
2	57	34

end0.0ms

sample531.0ms

Algorithm

intervals

Results

182.0ms	1737×	body	1280	valid
105.0ms	1253×	body	640	valid
99.0ms	4086×	body	80	valid
39.0ms	584×	body	320	valid
14.0ms	340×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6